Lindgren and Rue (2011) showed a link between Gaussian fields (GF) with covariance function of the Matèrn type with a GMRF whose precision matrix approximates well the inverse covariance matrix of the GF in some norm using a stochastic partial differential equation (SPDE) [1]}. The Matèrn covariance function between locations \(\mathbf {s}_i\)  and \(\mathbf {s}_j\)  in the \(d\) -dimensional space is given by
\( C(\mathbf {s}_i,\mathbf {s}_j)=\dfrac{\sigma ^2}{2^{\nu -1}\Gamma (\nu )} (\kappa \left\Vert \mathbf {s}_i-\mathbf {s}_j\right\Vert )^{\nu }K_{\nu }(\kappa (\left\Vert \mathbf {s}_i-\mathbf {s}_j\right\Vert ))\) 
